Non-linear System of Equations

Algebra Level 3

x+log⁡(x)=y−1y+log⁡(y−1)=z−1z+log⁡(z−2)=x+2 \begin{aligned} x+\log{(x)} = y-1\\ y+\log{(y-1)} = z-1 \\ z+\log{(z-2)} = x+2 \\ \end{aligned}

There is only one solution set (x,y,z)\left(x,y,z\right) to the system of equations above. Evaluate x+y+zx+y+z.

Note: Take the base of the logarithms as 10.

Image Credit: Wikimedia Thoma Loneliness.
Steven Zheng by Steven Zheng
×

Problem Loading...

Note Loading...

Set Loading...